Given the training set of Section REF , we train a GCNN [1]} to predict the field of physical values \(\textbf {y}\)  given a mesh \(\textbf {x}\) , as depicted by Fig. REF . The forward pass through a single layer can be written as
\(\widetilde{\textbf {u}}_{i}^{j} = \frac{1}{|\mathcal {N}(j)|} \sum _{n \in \mathcal {N}(j)} \frac{1}{K} \sum _{k=1}^{K} \textbf {w}_{k}(\textbf {v}_{i}^{j, n}) \otimes \Theta _{k} \textbf {u}_{i}^{j}\) 
